To verify the Work-Kinetic Energy theorem with a spring and cart apparatus.
Apparatus:
Our set-up required -
a rolling-cart with a wooden block, (m = 709-g)
a track for the cart,
a spring,
a position sensor, and
a force sensor.
The track provided a foundation for the entire experiment, as it was used to roll the cart on its surface.
We secured the force-sensor to the left end of the track using a clamp and a pole. We then attached a spring - one side to the secured force-sensor and the other side to the cart. At the right end of the track we placed a position sensor, which we programmed to take the origin of its measurements from the left end of the track.
Experiment:
To start, we set the left side of the track to be the origin (x = 0).
We pulled cart away from the force sensor (toward the right) and began collecting data as soon as the cart was released.
When the cart was released, it moved with some velocity toward the left and this velocity was captured through the motion detector.
After running the experiment and collecting data, we needed to analyze what had occurred.
We first recognized that the force sensor gave us a direct value for the force applied by the spring.
With this knowledge, we were able to create a Force-vs-Position graph, which gave us the work done by the spring when integrated over a certain interval.
We also added a calculated column for the Kinetic Energy at any given point using the known mass and the "velocity" variable from the motion detector.
We analyzed three separate sections of our graph by comparing the work done by the spring and the kinetic energy at three specific locations.
Our results:
1st -
Integral: 0.8197 N*m
Kinetic Energy: 0.636 J
2nd -
Integral: 1.203 N*m
Kinetic Energy: 1.164 J
3rd -
Integral: 1.556 N*m
Kinetic Energy: 1.331 J
Conclusion:
With slight uncertainty, we found that the work done on a cart by a spring is equal to the change in kinetic energy.
A Great Day for Physics.
(10/01/14 6:57 am)
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